American Mathematical Society

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 2816390
Full text of review: PDF This review is available free of charge.
Book Information:

Authors: Robert J. Daverman and Gerard A. Venema
Title: Embeddings in manifolds
Additional book information: Graduate Studies in Mathematics, Vol. 106, American Mathematical Society, Providence, RI, 2009, xviii+468 pp., ISBN 978-0-8218-3697-2, US $75.00, hardcover

Alexander, J. W., An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. USA 10 (1924), 8-10.

Alexander, J. W., Remarks on a point set constructed by Antoine, Proc. Nat. Acad. Sci. USA 10 (1924), 10-12.

Paul Alexandroff, Elementary concepts of topology, Dover Publications, Inc., New York, 1961. Translated by Alan E. Farley. MR 0149463

F. D. Ancel and J. W. Cannon, The locally flat approximation of cell-like embedding relations, Ann. of Math. (2) 109 (1979), no. 1, 61–86. MR 519353, DOI 10.2307/1971267

Antoine, L., Sur l’homeomorphie de deux figures et de leurs voisinages, J. Math. Pures Appl. 86 (1921), 221-325.

R. H. Bing, An alternative proof that $3$-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37–65. MR 100841, DOI 10.2307/1970092

R. H. Bing, Approximating surfaces from the side, Ann. of Math. (2) 77 (1963), 145–192. MR 150744, DOI 10.2307/1970203

R. H. Bing, Conditions under which a surface in $E^{3}$ is tame, Fund. Math. 47 (1959), 105–139. MR 107229, DOI 10.4064/fm-47-1-105-139

R. H. Bing, A surface is tame if its complement is $1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 131265, DOI 10.1090/S0002-9947-1961-0131265-1

J. W. Cannon, Shrinking cell-like decompositions of manifolds. Codimension three, Ann. of Math. (2) 110 (1979), no. 1, 83–112. MR 541330, DOI 10.2307/1971245

C. Carathéodory, Über die gegenseitige Beziehung der Ränder bei der konformen Abbildung des Inneren einer Jordanschen Kurve auf einen Kreis, Math. Ann. 73 (1913), no. 2, 305–320 (German). MR 1511735, DOI 10.1007/BF01456720

Robert D. Edwards, The topology of manifolds and cell-like maps, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 111–127. MR 562601

Robert D. Edwards, Demension theory. I, Geometric topology (Proc. Conf., Park City, Utah, 1974) Lecture Notes in Math., Vol. 438, Springer, Berlin, 1975, pp. 195–211. MR 0394678

Edwin E. Moise, Affine structures in $3$-manifolds. IV. Piecewise linear approximations of homeomorphisms, Ann. of Math. (2) 55 (1952), 215–222. MR 46644, DOI 10.2307/1969775

Edwin E. Moise, Affine structures in $3$-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96–114. MR 48805, DOI 10.2307/1969769

John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481–488. MR 149457

John R. Stallings, Polyhedral homotopy-spheres, Bull. Amer. Math. Soc. 66 (1960), 485–488. MR 124905, DOI 10.1090/S0002-9904-1960-10511-3

M. A. Štan′ko, Approximation of the imbedding of compacta in a codimension larger than two, Dokl. Akad. Nauk SSSR 198 (1971), 783–786 (Russian). MR 0284994

Review Information:

Reviewer: James W. Cannon
Affiliation: Brigham Young University
Email: cannon@math.byu.edu

Journal: Bull. Amer. Math. Soc. 48 (2011), 485-490
DOI: https://doi.org/10.1090/S0273-0979-2011-01320-9
Published electronically: March 4, 2011
Review copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.